The low-temperature specific heat in single crystals of orthorhombic YBa2Cu3O7−δ

Synthetic Metals, 29 (1989) F641-F650

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THE LOW-TEMPERATURE SPECIFIC HEAT IN SINGLE CRYSTALS OF ORTHORHOMBIC YBa2CusOT-~

H.B. BROM, and J. BAAK Kamerlingh Onnes Laboratorium, Leiden University, Postbus 9506, 2300 RA LEIDEN, The Netherlands A.A. MENOVSKY, M.J.V. MENKEN Natuurkundig Laboratorium, Universiteit van Amsterdam, Postbus 20215, 1000 HE AMSTERDAM, The Netherlands

ABSTRACT The low temperature specific heat, C, between 0.4 K and 30 K has been determined in orthorhombic single crystals of YBa2CusOT_s, with a transition temperature of 8g K. The various terms in the fit to these data are compared to similar data in related compounds and correlated to the results from conductance and resonance measurements in these materials. The interpretation of the linear temperature contribution in C, especially in terms of localized states and the RVB state, is discussed in relation to the other data; in the simplest fitting expression C "= aT °'4 + dT s, there is no need for a linear term. A too large number of allowed parameters hinders a definite statement about the presence of domain-wall excitations (dyadons) in the investigated samples.

INTRODUCTION After the first studies on the high temperature superconductor YBa2CuaO~ a discussion started about the consistency of the results from various techniques, like specific heat, susceptibility, field dependence of the transition temperature and conductance [1,2]. The coefficient of the electronic specific heat, the Sommerfield constant ~/, is e.g. in the weak-coupling limit related to Hc via (AC)To = 1.43-/T = i~oT,(dH,/dt)r " where H, can be expressed in Hcl a n d / o r H,2, while in a free electron model ~/ = ~(lrkB/l~s)2Xs; the spin susceptibility is here denoted by Xs. Initial powder values for ~/were between 3 and 12 mJ/molCuK 2 [3,4,5]. As was realized from the beginning, the presence of inhomogeneities in the ceramics could have influenced some of the results. This problem presumably might be circumvented by the use of single crystals; but even this is not a guaranty for single phase, as is illustrated by the results of Inderhees et al. [6,7]. At Tc = 90 K one single crystal shows only a third of the specific heat anomaly of the other, which means that even in one single crystal differences in e.g. oxygen content might exist. Concerning the low temperature specific heat, there is a similar 0379-6779/89/$3.50

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problem of sample quality. The quantity measured here is in principle an excellent probe to show the presence or absence of electronic excitations below the superconducting transition temperature, but the effect of contaminations or defects has to be excluded. The first powder measurements showed - apart from the usual lattice contribution which goes with the third power in the temperature - a non-negligible linear term around a few K [8,9,10,11]. The values of this ~-contribution were slightly sample dependent, with an average value of 10 m J / m o l K 2 for the superconducting orthorhombic compound. More scatter is present in the given values for the tetragonal modification of the YBa~CusOT-s ceramic: 5 < -y < 20 m J / m o l K 2. Recently yon Moinar et ah [12] determined the heat capacity of a mosaic of various single crystals. For the linear term in the Or-compound a value similar to the previous powder result was found. For the oxygen deficient states the linear term decreases with decreasing oxygen content, as does To. In this respect comparison of the high Tc superconductors YBa2CusOT_~ (YBaCuO) and La2_,(Sr/Ba),CuO, (LaBaCuO or LaSrCuO) with BaBil_,Pb,Os (BaBiPbO) or Lil+,Ti,_,O4 (LiTiO) are revealing, see table 1. After the discovery of superconductivity in BaBil-zPbzO by Sleight et al. [13] in 1975, for Pb-concentrations x -- 0.05 through 0.30, the material attracted special attention because of its composition (only non-transition elements) and relatively high transition temperature (To = 13 K for x -- 0.25, compare LaBa/SrCuO). Originally no specific heat anomaly was detected [14] while the electronic specific heat coefficient "~, obtained from the specific heat in the normal state was as small as 1 mJ/mol K -1. For the Debye temperature 8D a value between 166-195 K was calculated. The (electronic) specific heat in the lowest temperature range was found to be above the expected BCS-value: between 1 - ¼ of the normal electronic specific heat remains. Later on [15] in single crystals a narrow transition was observed only for x :- 0.25 and the Sommerfield constant % evaluated in 3 different ways, was confirmed to be as small as 1.5 m J / m o l K ~. In the ternary spinel system Li1+sTi2-xO4 [16,17,18], the superconducting transition temperature is the highest for the pure z

-

0 compound: T~ ~ 13 K: T~ decreases, as in

YBa2CusOT-s, when going away from the z -- 0/6 -- 0 composition. The "t-value found for LiTi2Os.~5 amounts to 21.4 mJ/molK2; the Debye temperature is about 685 K. Both T~, -y and 0v-values decrease with increasing x-value for 0 < z _< 0.I. There is hardly any indication of a residual electronic contribution in the specific heat far below Tc for the superconducting compounds, but for the non-superconducting LiL2Til.sO4 a Schottky anomaly attributed to 2 tool% impurities and a linear contribution ~ ~ 3.6 m J / m o l K 2 show up. For the ~-term in BaBiPbO Itoh [14] mentioned the now familiar possibilities of gapless superconductor with a finite density of states of normal electrons in the superconducting gap; residual normal state regions or a special distribution of 2 level energy splittings. After 2 years of high Tc superconductors also new explanations have been brought forward. In the RVB model [19] spinons i.e. spin excitation which closely resemble ordinary electrons, but have no charge, can be excited at all temperatures and will be visible by a linear specific heat term.

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Table 1

compound

T¢

Meissner

"~(T • To)

"~(T <~ To)

~

el>

(K)

fraction

( m J / m o l . K s)

( m J / m o l . K 2)

(m J/tool.K4)

(K)

a.=0

11

0.9

21.4

< 1.0

0.043

685

x -----0.05

11

0.6-0.9

19.7

0.5

0.054

630

x = 0.10

11

0.3

10.9

?

0.097

520

x--0.2

(3.6)

0.05

650

LII+fTi,_,O4

0

YBa2 CusOT_, z < 0.I0

90

0.5

a,b

8-10

0.4

410

x -- 0.3-0.5

60

0.3

a

(5)

0.5

380

a

5-20

0.8

3O0

?

0.6

?

0.42

166 ¢

x>0.6

(0)

BaPbl_fBi,Os x=

0.0

(0.45)

x = 0.20

10.7

?

1.2

?

0.29

189

x = 0.25

11.7

~ 1

1.6

0.3-0.4

0.26

195

x = 0.30

11.3

?

1.0

?

0.37

173

LaffiBal_ffiCuO4 x = 0.01

(0)

-

0

0.26

180 ¢

x = 0.05

5

0.2

?

5

0.26

180

x = 0.10

30

0.3

?

5

0.26

180

x = 0.15

30

0.5

11-12 d

5

0.26

180

* only indirect; e.g. in A C = a ' y T a depends on the coupling strength, see text. bfora

:

2.7(cp. P b ) - y = 1 4 m J / m o l K 2.

¢ these values are calculated with n = l , see text. d from

AC~ assuming

weak coupling (a = 1.43).

In a different approach the fitting procedure with a linear and cubic t e m p e r a t u r e term, C

=

b T + d T s, has to be abandoned and replaced by C

= e T ~. T w o dimensional twin

b o u n d a r y excitations (dyadons) are the origin for this dependence [20,21]. Especially t h e possibility of these 2 dimensional excitations the presence of which might be p r o m o t e d by b e t t e r crystals, has been the reason for our single crystal study at low temperatures (T _< 30 K).

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LOW TEMPERATURE SINGLE CRYSTAL SPECIFIC HEAT OF YBa~CusOT-8 The specific heat was measured using a thermal relaxation technique. A mosaic of about 80 single crystals with a total weight of about 60 mg was mounted on a sapphire plate, on which a heater of NiCr was sputtered. As thermometer a slice of a Speer carbon resistor was used. The plate with overall heat capacity C was connected via a small Cu-wire (with thermal resistance R) to a heat sink. The duration of the heat pulse was always chosen to be much larger than RC. The set-up is completely digitized and improvement of the signal to noise is easily achieved by averaging. In its present form the available temperature range is between 0.4 K and room temperature. Method and set-up were checked via a run with a Pd-sample. No deviations from the literature values were found.

D

B

I0"

i0 -" s

B

o

i0 "s

o

0

10

-6

mmmo oO

~ o°e

5

D

Io ° T

5 (K

lo'

) )

Fig. 1. Low-temperature specific heat, C, as a function of temperature, T, on a double logarithmic scale, showing the absolute values of the sample specific heat.

The samples were mounted with a precisely determined amount of Apiezon N- grease, which was also measured in the run with the empty apparatus to facilitate a correct subtraction of its heat capacity. The data after subtraction for the empty apparatus with the Apiezon-N grease are given in fig. 1 on a double logarithmic scale. The ratio of the empty apparatus to the sample heat capacity varied between 0.05 (at 0.4 K) and 2.5 (around 7 K). The samples, which showed full diamagnetic shielding, had a transition temperature at 89 K (midpoint) with a width of I K.

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I0'

b

2 / /

LO °

B z~ i,] ¸L

i0 ~ 5

LO ~

~

5

liY

L

'

'

~,

' '!0°

~:

Fig. 2. C per mol vs T on a double logarithmic scale: The fit in (a) is based on the expression C

=

toC

a T 1-a +

bT + cT s, while the fit in (b), which is confined to T <

8 K corresponds

= a T *-a + c T 2.

DISCUSSION OF THE EXPERIMENTAL DATA Fig. 2a and 2b show our data together with fits based on the expressions C = a T 1-~ + + b T + d T s (fig. 2a) and C = a T 1-~ + c T 2 (fig. 2b). The usual expression with the cubic

temperature term gives a b-value of (4.8 m J / m o l K 2) and a d-term of 0.57 mJ/molK4; in the first term a ~

1.05 and a ~

0 . 6 . 1 0 -2 m J / m o l K - % An equally good fit is obtained with

b = 0 (!), a = 0.012 m J / m o l K - ~ and ~ = 0.58 and d = 0.59 m J / m o l K 4. In the second fit, which is only applied between 0.4 and 8 K, the values found are a = 1.17, a = 0.7.10 -~ ( m J / m o l K -a) and c - 3.9 (mJ/molKS). The a T l - a - t e r m Incorporation of this term in the fitting expression improves the fit below 1 K. The measured temperature range below 1 K is too small to give a clear identification of this contribution. Several possiblities can be mentioned, all based on the high-temperature tail of Schottky anomalies, e.g. due to antiferromagnetic coupling [22], crystal field effects of the Cu(1)-ions being in an almost fourfold planar surrounding [23], and minigaps in the electronic structure [24]. To these we like to add the mechanism of random exchange between spins e.g. on the interrupted Cu(1)-chain. Concerning the last possibility the similarity with the specific heat of Quinolinium-TCNQ2 [25] is striking, which is the reason to present the lowtemperature contribution in this form. The presence of a two-level system leading to such a Schottky anomaly is supported by acoustic measurements [26]. We like to stress that the term with (1 - c~) = 0.42 together with the lattice term is sufficient to fit the whole investigated temperature range. Also in LaLssSr0.,6CuO4-~ an excellent fit was obtained with a similar expression (1 - c~) = 0.5 without a bT-term [22].

[0

F646 The bT-term and the presence of localized states By oxygen depletion of the g0 K superconductor YBa2CusOT-6 the inplane conductance changes from metallic to semiconducting. These results are similar to those obtained in Lil+zTi2-,O4 or e.g. Lal-zCrzOs and La1-,CozOs as a function of x and can be seen as a sign of decreasing charge carriers and increasing disorder in these compounds [27]. Due to these 2 factors charge carriers might be localized. In low dimensional systems, like YBaCuO or LaSrCuO and LaBaCuO localized electronic regions of sufficient extension might be formed. The linear contribution to the specific heat is then accounted for by these localized regions. Around the threshold from non-metallic to metallic one expects a large number of disconnected regions to exist. For LiTiO this argument is supported by the absence of the b-term (-y- term) ~or z = 0 and its presence for z :> 0.2. In LaSrCuO or LaBaCuO the situation is more complicated because the creation of a sufficient number of charge carriers to reach the threshold value is accomplished only by the simultaneous introduction of disorder. Cu-NMR data fit such a localized state picture quite well. The relaxation rate of the 31 MHz Cu NMR line is found to decrease drastically by oxygen depletion in the chain. Because the 31 MHz Cu-nuclei are located in the Cu(2)O-plane (see e.g. Walstedt et al. [28]) Warren et al. [2g] conclude from this decrease that the metallic character and spin density are effectively eliminated for at least a subset of the planar Cu-sltes. In such a picture isolated metal-like regions might be formed that are separated from other metallic ones by inactive domains so that only via hopping these isolated regions can participate in the conduction process. These are then to be identified with the localized regions giving rise to the bT-term. The precise connectivity of the active regions will depend on the way oxygen depletion is accomplished, e.g. via quenching or Zr-reduction. This explains the spread found especially in the tetragonal samples. For a 6 ~ 0 sample no such regions are expected and in that sense the results of yon Molnar et al. of b =

g mJ/molK ~ [12] and our result b =

4.8

mJ/moIK 2 are not straightforward to interpret.

The bT-term and the RBV-state Kumagal et al. [30] studied systematically the ~-term in LaBCO as a function of Ba~ concentration. From the correlation between magnetic order and vanishing ~T-terms and the existence of a finite ~T-term for Ba-doping, they see support for the Resonating Valence Bond (RYB) picture. Also the small change in the Y-relaxatlon rate going from orthorhombic superconducting to tetragonal non-superconducting YBCO [32] can be reconciled with the RVB model. Especially the presence of a ~/-term in the 6 =

0 samples is more easily to

understand in the RVB-model, than in t~he Zlocalized" picture. A problem which still has to be solved concerns the magnetism in LiTiO and BaBiPbO,

F647

which depending on concentration show both also a linear contribution in the specific heat. Disorder leading to localized states do not need magnetism as a prerequisite and can be present in all these oxide materials.

The dTS-term and the Debye temperature The proportionality constant d of the TS-term is related to the Debye temperature 0v as d =

12 7r4nR/5 #sv, where n is often taken to be the number of atoms in a unit cell and

R is the gas constant. Because the Debye temperature is a measure of the cut-off energy of the collective lattice vibrations, the internal motion in complexes should be neglected. As an example in yttrium ethyl sulfate, Y(C2HsSO4)s.9H20, it is the collective motion of the metal ions and the water molecules and sulfate and ethyl radicals moving as units that determine 0v [31]. F o r B a B i P b O Itoh[14] u s e s n

=

l and obtains 1 6 6 K <

0D < 1 9 5 K for the

various Ba, Bi concentrations. Using the same formula in YBCO e.g. yon Molnar et al. [12], taking n =

13, i.e. equal to the number of atoms in the unit cell, arrive at 8v ~ 400 K.

A better choice is to consider at least the Cu-O units as an entity (see also [33]). To avoid confusion only d-values will be compared. It appears that increasing the oxygen deficiency in the chains increases d: from about 4 × 10-4(6 ~ 0) to 8 × 10-4(6 > 0.5). Our value for d, based on the fit shown in fig. 2a is 5.7 x 10 -4 m J / m o l K 4.

The c T L t e r m and the presence of dyadons In LaSrCuO or LaBaCuO, and YBCO the low temperature specific heat analysis is mostly confined to the region below 10 K. If a larger region is inspected, in some experiments a change of the cubic contribution is seen, which is one of the experimental predictions of the dyadon model [20,21]. Another way of dealing with this upturn is the introduction of a low lying Einstein oscillator [34], which adds to the lattice (Debye) specific heat. Without the freedom given by this Einstein oscillator, it is already difficult to discriminate between the expressions used. There is however no principal reason why the second expression cannot be modified into C

=

a T 1-~ + c T ~ + dT s because although the 2 dimensional dyadon excitations

take over the 3-dimensionai lattice contribution, the number of domains might vary widely between different crystals (we measure a mosaic), or even different parts of the same crystal. The inclusion of an Einstein oscillator gives another degree of freedom. The fit given in fig. 2b can certainly be improved by the inclusion of these allowed extra terms. Because of the many degrees of freedom we cannot confirm from these measurements alone the presence of dyadons (and the possible absence of the bT term).

Other e~citations Low lying Bose excitations have a dispersion curve w ~ dependence of the specific heat C

k v , which give a power law

0c T ~/v with d the dimensionality of the system and

F648 v ---- 1 for antiferromagnetic magnons. So excitations confined to the chain might lead to a linear temperature dependence. Also a distribution of 2-level splittings can give a similar behaviour. The origin for such a distribution in La(Ba,Sr)CuO is obvious, because the Sr ~+ or Ba 2+ ions tend to distort the Cu 2+ octahedrons towards a rhombohedral symmetry. Near a dopant ions, each Cu-Oe cage is subject to a two level system associated with the two possible configurations [35].

CONCLUSIONS By comparison of the linear term in the low temperature specific heat in YBaCuO with results of other compounds and other techniques the concept of localized regions and the RVB state are discussed. The main problem in the first interpretation is the relatively large value of ~/for ~ ~ 0; for a RVB-like model the magnetism in BaBiPbO or LiTiO must be clarified. To fit the results with a random-exchange like expression (aT 1-~) together with the usual lattice term is shown to be an excellent alternative. Concerning the 2-dimensional domain boundary excitations, the number of allowed parameters is too large to give an experimental verification via the specific heat method.

ACKNOWLEDGEMENTS This work is part of the program of the Leiden Materials Science Centre and ALMOS and is supported by the Foundation for Fundamental Research on Matter (FOM), which is sponsored by the Netherlands Organization for the Advancement of Pure Research (ZWO).

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